Constructions of homotopy 4-spheres by pochette surgery

TL;DR

This paper demonstrates that infinitely many homotopy 4-spheres constructed via pochette surgery are actually diffeomorphic to the standard 4-sphere, extending understanding of 4-manifold topology.

Contribution

It constructs infinitely many embeddings of pochettes into the 4-sphere and proves the resulting homotopy 4-spheres are all standard.

Findings

All constructed homotopy 4-spheres are diffeomorphic to the 4-sphere

Infinite embeddings of pochettes into S^4 are explicitly constructed

Pochette surgery does not produce exotic 4-spheres in these cases

Abstract

The pochette surgery, which was discovered by Iwase and Matsumoto, is a generalization of the Gluck surgery. In this paper we construct infinitely many embeddings of a pochette into the 4-sphere and prove that homotopy 4-spheres obtained from surgeries along these embedded pochettes are all diffeomorphic to the 4-sphere.